Solid-state lighting devices including light-emitting diodes (LEDs) and more particularly contact structures for LED chips are disclosed. LED chips as disclosed herein may include contact structure arrangements that have reduced impact on areas of active LED structures within the LED chips. Electrical connections between an n-contact and an n-type layer may be arranged outside of a perimeter edge or a perimeter corner of the active LED structure. N-contact interconnect configurations are disclosed that form electrical connections between n-contacts and n-type layers of LED chips outside of lateral boundaries of the active LED structures. By electrically contacting n-type layers outside of the lateral boundaries of the active LED structures, LED chips are provided with improved current spreading and improved brightness.